Error propagation during inverse modeling leads to spurious correlations and misinterpretation of lake metabolism

Inverse modeling is a common practice to decompose observed processes into constituents that are unobservable or difficult to measure. To achieve this goal, a mechanistic model is calibrated to fit the observations and thereby the model produces a coherent set of constituent estimates. A disadvantage of this procedure is that any disagreement between the model assumptions and reality potentially introduces bias and other statistical artifacts into the constituents and their relations. Lake metabolism is recently most often followed by high-frequency measurements of dissolved oxygen, and inverse modeling with simple conceptual models is used to couple oxygen dynamics to ecosystem-wide aggregated metabolic rates, such as net ecosystem production (NEP). These models rely on estimates of gas exchange and community respiration. Using a model of a simple ecosystem and field data, we demonstrate that typical relations between modeled metabolic rates frequently do not follow patterns expected from synthetic ecosystems and that estimation errors strongly influence calculations by producing strong, spurious correlations. Correlation artifacts can be expected during inverse modeling, whenever observed time series are decomposed into poorly known or unmeasured processes that can compensate for the effect of each other.